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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Homological algebra for the representation Green functor for abelian groups
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by Joana Ventura PDF
Trans. Amer. Math. Soc. 357 (2005), 2253-2289 Request permission

Abstract:

In this paper we compute some derived functors $\operatorname {Ext}$ of the internal homomorphism functor in the category of modules over the representation Green functor. This internal homomorphism functor is the left adjoint of the box product. When the group is a cyclic $2$-group, we construct a projective resolution of the module fixed point functor, and that allows a direct computation of the graded Green functor $\operatorname {Ext}$. When the group is $G=\mathbb {Z}/2\times \mathbb {Z}/2$, we can still build a projective resolution, but we do not have explicit formulas for the differentials. The resolution is built from long exact sequences of projective modules over the representation functor for the subgroups of $G$ by using exact functors between these categories of modules. This induces a filtration which gives a spectral sequence which converges to the desired $\operatorname {Ext}$ functors.
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Additional Information
  • Joana Ventura
  • Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
  • Email: jventura@math.ist.utl.pt
  • Received by editor(s): August 22, 2003
  • Published electronically: May 10, 2004
  • Additional Notes: The author was partially supported by FCT grant Praxis XXI/BD/11357/97 and a one year research grant from Calouste Gulbenkian Foundation
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 2253-2289
  • MSC (2000): Primary 55P91, 18G10
  • DOI: https://doi.org/10.1090/S0002-9947-04-03566-4
  • MathSciNet review: 2140440